Staffans O. — Well-Posed Linear Systems :: Электронная библиотека попечительского совета мехмата МГУ

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Staffans O. — Well-Posed Linear Systems

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Название: Well-Posed Linear Systems

Автор: Staffans O.

Язык:

Рубрика: Математика/Математическая Физика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 871

Добавлена в каталог: 25.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(X+BU)_{1}$       229 230 297 303—305 308
$1_{+}$       xvi
$A\geq0$       xiv
$A\gg0$       xiv
$A^{-*}$       126
$A^{h}$       141—143
$A^{\odot}$       127 129
$A_{\alpha}$       141 142
$A_{|X_{n}}$       134 135
$BC^{n}_{\omega}$ , $BC^{n}_{\omega,loc}$ , $BC^{n}_{0,\omega}$ , $BC^{n}_{0,\omega,loc}$       99
$BC_{0}$ , $BC_{0,\omega}$ , $BC_{0,\omega,loc}$       xvii 65
$BUC^{n}_{\omega}$ , $BUC^{n}_{\omega,loc}$       99
$BUC_{\omega}$ , $BUC_{\omega,loc}$       65
$C\&D$       xv
$C^{\beta,h}$       323—325
$C_{\alpha}$       323 324
$C_{\mid(X+BU)_{1}}$       310 312 313 316
$E_{\omega}$       xvi
$H^{2}$       619
$H^{p}$       628
$H^{\infty}$       619 628—634
$J^{h}$       141 142 318
$J^{\beta,h}$       318—320 324 325
$J_{\alpha}$       141 142 318 319 324
$l^{1}$       813
$L^{2}$       84 87 88 90 297
$L^{p}$ , $L^{\infty}$       xvii
$L^{p}$ -well-posed      38
$l^{p}_{0,r}$       764
$l^{p}_{0,r}$ -bounded      764
$L^{p}_{c,loc}$       38
$L^{p}_{loc,c}$       360
$l^{p}_{r}$       764
$L^{p}_{\omega}$ , $L^{p}_{\omega,loc}$ , $L^{p}_{0}$ , $L^{p}_{0,\omega}$ , $L^{p}_{0,\omega,loc}$       xvii 65
$L^{p}|$ Reg      xviii 40
$L^{p}|$ Reg-well-posed      8 40
$L^{p}|Reg_{0}$       40
$L^{\infty}$ -well-posed      39 40 242 243
$Reg^{n}$       xvii
$Reg_{0}$ , $Reg_{0,\omega}$ , $Reg_{0,\omega,loc}$       xvii 65
$Reg_{loc,c}$       360
$Reg_{\omega}^{n}$ , $Reg_{\omega,loc}^{n}$ , $Reg_{0,\omega}^{n}$       99
$TIC^{p}_{\infty}$ , $TIC^{p}_{loc}$       74
$TIC^{Reg}$ , $TIC^{Reg}_{omega}$ , $TIC^{Reg}_{\infty}$       74
$TI^{p}_{\omega}$ , $TIC^{p}_{\omega}$       73
$TI^{Reg}$ , $TI^{Reg}_{\omega}$ , $TI^{Reg}_{loc}$       74
$W^{n,p}$       xvii
$W^{n,p}_{\omega}$ , $W^{n,p}_{loc}$ , $W^{n,p}_{0,\omega}$ , $W^{n,p}_{c,loc}$ , $W^{n,p}_{\omega,loc}$       99
$W_{k}$       301
$X^{\odot}$       127 129
$X_{n}$       xv 134—136
$X_{n}^{\ast}$       xv
$X_{\alpha}$       161
$Я_{h}$       362
$[^{X}_{U}]$       xvi
$\Delta$       310—314 316
$\Delta_{\delta}$       164
$\dot{+}$       xvi
$\gamma$       xvi 162 310 312 314 316
$\gamma_{\lambda}$       xiv 55
$\langle x,x^{*}\rangle$       xiv 124
$\mathbb{C}$ , $\mathbb{C}^{+}$ , $\mathbb{C}^{-}$ , $\overline{\mathbb{C}}^{+}$ , $\overline{\mathbb{C}}^{-}$       xiii
$\mathbb{C}^{+}_{\omega}$ , $\mathbb{C}^{-}_{\omega}$ , $\overline{\mathbb{C}}^{+}_{\omega}$ , $\overline{\mathbb{C}}^{-}_{\omega}$       xiii
$\mathbb{D}^{+}$ , $\overline{\mathbb{D}}^{+}$ , $\mathbb{D}^{-}$ , $\overline{\mathbb{D}}^{-}$       xiii
$\mathbb{D}^{+}_{r}$ , $\overline{\mathbb{D}}^{+}_{r}$ , $\mathbb{D}^{-}_{r}$ , $\overline{\mathbb{D}}^{-}_{r}$       xiii
$\mathbb{F}_{t}$       84—85
$\mathbb{R}$ , $\mathbb{R}^{+}$ , $\overline{\mathbb{R}}^{+}$ , $\mathbb{R}^{-}$ , $\overline{\mathbb{R}}^{-}$       xiii
$\mathbb{T}$       xiii
$\mathbb{T}_{T}$       xiii
$\mathbb{Z}$ , $\mathbb{Z}^{+}$ , $\mathbb{Z}^{-}$       xiii
$\mathcal{B}(U)$       xiv
$\mathcal{B}(U;Y)$       xiv
$\mathcal{D}(A)$       xiv
$\mathcal{D}(A\&B)$       229
$\mathcal{D}(\widetilde{C})$ , $\mathcal{D}(\overline{C}^{\beta})$       327 328 336
$\mathcal{D}(\widetilde{C}_{\omega})$       342
$\mathcal{N}(A)$       xiv
$\mathcal{R}(A)$       xiv
$\mathfrak{A}^{d}$       366
$\mathfrak{A}^{t}$       34 35 38 61 62
$\mathfrak{A}^{t}_{s}$       5 41 43 46 48 71 360 362—364
$\mathfrak{A}^{\dag}$       364 365
$\mathfrak{A}^{\odot}$       127 129
$\mathfrak{A}_{|X_{n}}$       134 135
$\mathfrak{B}$       32 34 35 38 61 62 80 85 211 212
$\mathfrak{B}^{d}$       366
$\mathfrak{B}^{t}$       5 41—43 45 66 71 363
$\mathfrak{B}^{t}_{s}$       5 32—34 41—43 46 48 71 360 362—364
$\mathfrak{B}^{\dag}$       364 365
$\mathfrak{B}_{s}$       362
$\mathfrak{C}$       32 34 35 38 61 62 80 85 211 212
$\mathfrak{C}^{d}$       366
$\mathfrak{C}^{t}$       362
$\mathfrak{C}^{\dag}$       364 365
$\mathfrak{C}_{s}$       5 32—34 41—43 45 71 360 363
$\mathfrak{C}_{s}^{t}$       5 41—43 46 48 362—364
$\mathfrak{D}$       32 34 35 38 61 62 80 85 211
$\mathfrak{D}^{d}$       366
$\mathfrak{D}^{t}$       5 41—43 45 362 363
$\mathfrak{D}^{t}_{s}$       5 41—43 46 48 362—364
$\mathfrak{D}^{\dag}$       364 365
$\mathfrak{D}_{s}$       5 32 34 41—43 45 71 360 362 363
$\odot$ -dual      129
$\omega_{\mathfrak{A}}$       66 70
$\oplus$       xvi
$\overline{C\&D}^{\beta}$ , $\overline{C\&D}^{\beta}_{w}$ , $\overline{C\&D}^{\beta}_{s}$       338
$\overline{C}^{\beta}$       326—328 334 336
$\overline{C}^{\beta}_{w}$ , $\overline{C}^{\beta}_{s}$       326
$\Phi_{t}$       84—85
$\pi_{+}$       xiv 38
$\pi_{-}$       xiv 38
$\pi_{J}$       xiv 33 38 65
$\Psi_{t}$       84—85
$\rho(A)$       xv 102
$\sigma(A)$ , $\sigma_{p}(A)$ , $\sigma_{r}(A)$ , $\sigma_{c}(A)$       xv 102
$\sum^{d}$       351 366 374
$\sum^{\dag}$       366
$\sum_{\theta,\gamma}$       164—166 169
$\tau^{t}$       51 53 66 99 107 110 131 192 193
$\tau^{t}_{+}$       51 53 66 99 107 110 131 192 193
$\tau^{t}_{-}$       51 53 66 99 107 110 131 192 193
$\tau^{t}_{[0,T)}$       51 52 54 66 99 107 110 131 192 194
$\tau^{t}_{}\mathbb{T}_{T}$       52 99 100 107 110 131 193 194 471
$\widetilde{C\&D}$ , $\widetilde{C\&D}_{w}$ , $\widetilde{C\&D}_{s}$       338
$\widetilde{C}$       326—328 334 336
$\widetilde{C}_{\omega}$ , $\widetilde{C}_{s}$       326
0      xiii
1      xiii
A&B      xv
A*      xiv 124 125
Abel approximation      142 318 324
Abel extension      326 338
Abstract boundary condition      313
Abstract elliptic problem      313
Abstract partial differential operator      313
Admissibility based on duality      623—627
Admissibility based on Lax — Phillips model      665—668
Admissibility in $L^{1}$       623 626
Admissibility in Reg      623 626
Admissibility infinite time      619
Admissibility, contraction semigroups      656—664
Admissibility, diagonal semigroups      651—655
Admissibility, Hilbert space case      628—634
Admissibility, normal semigroups      651—655
Admissible definition      619—622
Admissible, A-admissible      204—205
Admissible, control operator      21 620 621
Admissible, jointly      21 488 621
Admissible, observation operator      21 620 621
Admissible, observation/feedthrough operator      620 622

Admissible, output feedback operator      17 442 443
Admissible, output injection pair      455 456
Admissible, state feedback pair      454 455
Analytic group      94
Analytic semigroups      11
Annihilator      586
Anti-causal      15 73 359—364
Anti-causal dual      15
Anti-Hankel operator      73
Anti-Toeplitz operator      73
Approximation of identity      141 142 318—325
Approximation of observation operator      323—325
Approximation of semigroup      141—143
Available storage      26 750 758
B      214—232
Backward state trajectory      360
Backward state transition map      362
Backward wave operator      81
Backward, input map      362
Backward, input/output map      362
Backward, output function      360
Backward, output map      362
Balanced      20
Balanced realization      21 574—582 752
Balanced, bounded real      26 759
Balanced, passive      26 752 759
BC, $BC_{\omega}$ , $BC_{\omega,loc}$       xvii 65
Beta function, xvi      159 319 320
Bezout identity      19
bi-inner      24 681
BMO      659 661
BMOA      660 661
Boundary control node      308—317
Boundary control system      14 50 308—317
Boundary/distributed control node      315—317
Boundary/distributed control system      315—317
Bounded      478
Bounded control operator      11
Bounded group      118
Bounded observation operator      12
Bounded output      478
Bounded real balanced      759
Bounded semigroup      118
Bounded, $\ell^{p}_{r}}$ -bounded      764
Bounded, $\omega$ -bounded      70 75 564 566 568 571 620 632 633 665
Bounded, $\omega$ -bounded, jointly      621 633 666
Bounded, input      477
Bounded, input-state      477
Bounded, input/output      477 498
Bounded, state-output      477
Bounded, state-state      477
BUC      xvii
C, $C^{n}$       xvii
Carleson measure      22 644—650
Cascade connection      448 449
Cascade connection compatible      471
Cascade connection stabilizable      497
Cauchy formula      155
Cauchy problem      10 12 146—153
Causal      73
Causal dual      15
Causality condition      36 43 45 79 363
Cayley transform      28 123 775—787
Central controller      531
Cesaro approximation      142 143 318 319 324
Cesaro extension      326 356
Cesaro mean      356
Chain scattering transformation      17 415—430 432
Characteristic function      xvi 25 713
Closed range      603
Closed range of Hankel operator      545 608 609
Closed-loop generators      458—470
Closed-loop sensitivity      438
Closed-loop system      17 435
Closed-loop system, compatible      467—468
Closed-loop system, dual      470
Closed-loop system, regular      468—474
Closed-loop, observation/feedthrough operator      458
Closed-loop, system node      458
co-energy preserving      680 686
co-generator      28 782
co-isometric dilation      702
co-isometric operator      803
co-lossless system      694—701
Coercive      602
Combined observation/feedthrough operator      12 249
Compatible closed-loop system      467—469
Compatible extension      326
Compatible flow-inverted system      389—391
Compatible node      309
Compatible partial flow-inversion      427—428
Compatible realization      309
Compatible system      13 299—307 309 318 342 355 374 392
Complementary sensitivity      439
Complemented subspace      196
Completely non-unitary      680 684
Completely nonunitary      24
composition      43 45 363
Compression      25 702 715
Conservative extension      715—720
Conservative system      24 686—693
Contraction group      118
Contraction semigroup      118 656
Contractive purely      681
Control operator      3 11 26 214—232 263 762
Control operator injective      290
Control operator, $L^{1}$ -well-posed      218
Control operator, bounded      11 31 50 86 88 236 244 245 248 350 614
Control operator, determined by feedthrough operator      304
Control operator, dual      370
Controllability approximate      20
Controllability conditions      583—592
Controllability exact      564—573
Controllability gramian      21 22
Controllability of transformed system      598—601
Controllable      20 546
Controllable mode      593—595
Controller      19
Coprime detectability      19
Coprime factorizations      502—523
Coprime fractions      502—523
Coprime stabilizability      19
Coprime, left      502
Coprime, left, exponentially      502
Coprime, necessary condition      505
Coprime, right      489 490 502
Coprime, right, exponentially      502
Corona theorem      542
Cross product      56
Cross product, compatible      307
Cross product, dual      367
Cross product, stabilizable      497
Darlington synthesis      719
Datko's theorem      208
Decompositions of systems      290—296
Deficiency operator      23 678
Degree McMillan      589
Delay line      50 54 55 71 87 90 216 235 243 247 278 300 302 305 306 350 367 471 566
Denominator      502
Detectability      18 488—501
Detectability, left coprime      516
Detectability, meromorphic extensions      496
Detectability, necessary rank condition      495
Detectability, preserved under feedback      493 519
Detecting, coprime      511—523
Detecting, exponentially      520
Detecting, left coprime      516
Diagonal semigroup      112 129 178 207 283 285 642 643 651 653
Diagonal system      13 283—287 298 651
Diagram conventions      42

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